Sub-model identification in the context of flexible distributions obtained by perturbation of symmetric densities

Distributions obtained by perturbation of symmetric densities provide flexible models suitable to fit the distribution of data affected by departures from normality, in particular when such deviations are due to skewness and/or heavy tails.However, the adoption of these models may lead to inefficient estimators whenthe data are generated by a simpler distribution. Consequently a testingstrategy aimed at finding the most parsimonious model among non nested ones is proposed. Thecorresponding test statistics are slight modifications of well-knownones, and their asymptotic distributions do not depend on nuisanceparameters. The normality test is the final step of the procedure. Analytical results provide thestatistical properties of the proposed tests whereas their performance in finite sample is investigated through numerical experiments.